Pattern avoidance in alternating sign matrices
2007 (English)In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 11, no 04-mar, 471-480 p.Article in journal (Refereed) Published
We generalize the definition of a pattern from permutations to alternating sign matrices. The number of alternating sign matrices avoiding 132 is proved to be counted by the large Schroder numbers, 1, 2, 6, 22, 90, 394,.... We give a bijection between 132-avoiding alternating sign matrices and Schroder paths, which gives a refined enumeration. We also show that the 132-, 123-avoiding alternating sign matrices are counted by every second Fibonacci number.
Place, publisher, year, edition, pages
2007. Vol. 11, no 04-mar, 471-480 p.
alternating sign matrix, pattern avoidance, restricted permutations, Schroder numbers
IdentifiersURN: urn:nbn:se:kth:diva-17209DOI: 10.1007/s00026-007-0330-1ISI: 000252603800013ScopusID: 2-s2.0-43149098535OAI: oai:DiVA.org:kth-17209DiVA: diva2:335252
QC 201005252010-08-052010-08-05Bibliographically approved